This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem jaoi3

Description: Inference separating a disjunct of an antecedent. (Contributed by Alexander van der Vekens, 25-May-2018)

Ref Expression
Hypotheses jaoi3.1 ⊢ φ → ψ
jaoi3.2 ⊢ ¬ φ ∧ χ → ψ
Assertion jaoi3 ⊢ φ ∨ χ → ψ

Proof

Step Hyp Ref Expression
1 jaoi3.1 ⊢ φ → ψ
2 jaoi3.2 ⊢ ¬ φ ∧ χ → ψ
3 1 2 jaoi ⊢ φ ∨ ¬ φ ∧ χ → ψ
4 3 jaoi2 ⊢ φ ∨ χ → ψ